Variational symmetries of Lagrangians - Torres del Castillo, G.F.; Andrade Mirón, C.; Bravo Rojas, R.I. (Revista Mexicana de Física E, 2013)
We present an elementary derivation of the equation for the infinitesimal generators of variational symmetries of a Lagrangian for a system with a finite number of degrees of freedom. We also give a simple proof of the existence of an infinite number of Lagrangians for a given second-order ordinary differential equation.